If you add any of the name variants, make sure to edit it in the Add Index Entry dialog to make it the same. The index entry itself does not have to be the exact text as it appears in your document; it's just an invisible marker, which indicates the page number to appear in the final index.

Unifying the name in your plain text is totally unnecessary (although marking names for an index and then generating it is sure to spot a couple of mis-spellings).

For a name like this, you could go for either "Haynes, R.R." or "Haynes, Raleigh R.", or even "Haynes, Raleigh Rutherford" (to properly distinguish him from his father with the same initials, "Haynes, Robert Redford").